Question: When Hugo is serving at a restaurant, there is a $0.03$ probability that each party will request a high chair for a young child. During one hour, Hugo served $10$ parties. Assuming that each party is equally likely to request a high chair, what is the probability that at least one party will request a high chair? Round your answer to the nearest hundredth. $P(\text{at least one high chair})=$
Solution: Strategy In this situation it is much easier to calculate the probability of the event we are looking for (at least one party that requests a high chair) by calculating the probability of its complement (no parties request a high chair), and subtracting from $1$. In other words, we can use this strategy: $P(\text{at least one high chair})=1-P(\text{none of 10 with high chair})$ Calculations $\begin{aligned} &\phantom{=}P(\text{at least one high chair}) \\\\ &=1-P(\text{none of 10 with high chair}) \\ \\ &=1-(0.97)^{10} \\ \\ &\approx 1-0.7374 \\ \\ &\approx 0.2626\end{aligned}$ Answer $P(\text{at least one high chair}) \approx 0.26$